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C5×D7×D31⋊C3 #27189142

order13020
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D7×D31⋊C3

Splittings

Fitting, socle, HallC5×C7×C31 ⋊ C22×C3
derived, HallC7×C31 ⋊ C22×C3×C5
HallC5×D7×D31 ⋊ C3
HallC5×C7×C31⋊C3 ⋊ C22
HallD7×D31 ⋊ C3×C5
HallC7×C31⋊C3 ⋊ C22×C5
HallC5×C31⋊C3 ⋊ C2×D7
HallC5×C31 ⋊ C2×C3×D7
HallC31⋊C3 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C3×C5×D7
SylowC7 ⋊ C2×C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D7×D31⋊C3
commutator, cosocle, hypocenterC7×C31C22×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C31C22×C3
LCSG ▷ C7×C31
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 points:

(2,6,7,3,4,8)(5,14,15,9,10,22)(11,24,25,17,18,30)(12,23,19,20,16,13)(21,31,28,27,26,29)(32,33,35,37,38,36,34)(39,40,41,42,43);(1,2,5,11,19,7,6,12,21,28,15,23,14,18,26,25,30,31,24,10,16,22,29,27,20,4,8,13,17,9,3)(33,34)(35,36)(37,38)

Conjugacy classes & character table

275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 109);